Rough I-statistical convergence of sequences

Afrika Matematika, 2015

The notion of I-statistical convergence of a double sequence was first introduced by Belen et. al.[2] and the notion of rough convergence of a sequence was first introduced by Phu [19]. In this paper we introduce and study the notion of rough I-statistical convergence of double sequences in normed linear spaces. We also introduce the notion of rough I-statistical limit set of a double sequence and discuss about some topological properties of this set.

Malaya Journal of Matematik

The notion of I-statistical convergence of a double sequence was first introduced by Belen et. al.[2] and the notion of rough convergence of a sequence was first introduced by Phu [19]. In this paper we introduce and study the notion of rough I-statistical convergence of double sequences in normed linear spaces. We also introduce the notion of rough I-statistical limit set of a double sequence and discuss about some topological properties of this set.

Conference Proceedings of Science and Technology, 2020

In this study, we introduce the concepts of rough statistical cluster point and rough statistical limit point of a sequence in 2-normed space and investigate some properties of these concepts.

Honam Mathematical Journal, 2021

In this study, we introduced the notions of rough statistical convergence and defined the set of rough statistical limit points of a sequence and obtained statistical convergence criteria associated with this set in 2-normed space. Then, we proved that this set is closed and convex in 2-normed space. Also, we examined the relations between the set of statistical cluster points and the set of rough statistical limit points of a sequence in 2-normed space.

Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi

The aim of this paper is to we examine the notion of gradually rough I_((λ,μ) )-statistical convergence of double sequences in gradual normed linear spaces (GNLS). In addition, we define the concept of gradually rough I_((λ,μ) )-statistical limit set of double sequences and obtain some algebraic and topological features of this set. Theorems are proved in the light of GNLS theory approach. Results are obtained via different perspective and new examples are established to justify the counterparts and indicate existence of introduced notions. We produce significant results that present several fundamental properties of this notion. The results established in this research work supplies an exhaustive foundation in GNLS and make a significant contribution in the theoretical development of GNLS in literature. The original aspect of this study is the first wholly up-to-date and thorough examination of the features and implementations of new introduced notions in GNLS.

The Mathematical Association of Thailand

The main purpose of this work is to define rough statistical convergence in probabilistic normed spaces. We have proved some basic properties as well as some examples which shows this idea of convergence in probabilistic normed spaces is more generalized as compared to the rough statistical convergence in normed linear spaces. Further, we have shown the results on sets of statistical limit points and sets of cluster points of rough statistically convergent sequences in these spaces.

arXiv (Cornell University), 2024

In this paper, using the concept of natural density, we have introduced the notion of rough statistical convergence which is an extension of the notion of rough convergence in a partial metric space. We have defined the set of rough statistical limit points of a sequence in a partial metric space and proved that this set is closed and bounded. Finally, we have found out the relationship between the set of statistical cluster points and the set of rough statistical limit points of sequences in a partial metric space.

Filomat, 2019

In this study, we investigated relationships between rough convergence and classical convergence and studied some properties about the notion of rough convergence, the set of rough limit points and rough cluster points of a sequence in 2-normed space. Also, we examined the dependence of r-limit LIMr 2xn of a fixed sequence (xn) on varying parameter r in 2-normed space

Publications de l'Institut Math?matique (Belgrade), 2019

We introduce rough I-statistical convergence as an extension of rough convergence. We define the set of rough I-statistical limit points of a sequence and analyze the results with proofs.

arXiv: Functional Analysis, 2016

In this paper, we introduce the notions of pointwise rough statistical convergence and rough statistically Cauchy sequences of real valued functions in the line of A. (T$\ddot{u}$rkmenoglu) G$\ddot{o}$khan and M. G$\ddot{u}$ng$\ddot{o}$r \cite{Tu1}. Furthermore we study thier equivalence.